Noncommutative geometry in physics: A point of view

Nuclear Physics B - Proceedings Supplements

Volumn 104, Issue 1-3, 2002, Pages 143-149

  Lizzi, Fedele ^a,b  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^b Monte Sant’Angelo ^*  (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036461934     PISSN: 09205632     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0920-5632(01)01601-2     Document Type: Article

References (16)

1. A.H. Chamseddine and A. Connes, A universal action formula, Phys. Rev. Lett. 77 (1996) 4868, hep-th/9606056. The paper which introduced the spectral action principle
2. A. Connes, Noncommutative Geometry (Academic Press, 1994). "The" reference par excellence to Noncommutative Geometry. A beautiful book.
3. A. Connes, Noncommutative geometry and reality, J. Math. Phys. 36 (1995) 6194.
4. A. Connes, M.R. Douglas and A. Schwarz, Noncommutative geometry and matrix theory: Compactification on tori, JHEP 9802 (1998) 003, hep-th/9711162. The paper which connected NCG with the matrix models of strings.
5. M. Douglas and N. Nekrasov, Noncommutative field theory, hep-th/0106048. A review of field theories on a noncommutative space.
6. J. Frohlich and K. Gawedzki, Conformal field theory and geometry of strings, Lectures given at Mathematical Quantum Theory Conference, Vancouver, Canada, 4-8 Aug 1993, published in the proceedings, hep-th/9310187. The first paper to consider spectral geometry for strings in the context of NCG, and its connections with vertex operators.
7. J.M. Gracía, J.C. Várilly and H. Figueroa, Elements of Noncommutative Geometry, Birkhauser, 2000. Probably the most comprehensive book on the mathematics of NCG to date.
8. G. Landi, Noncommutative Spaces and their Geometries, Springer Lecture notes, 1997. A good introduction to Noncommutative Geometry
9. G. Landi, F. Lizzi and R.J. Szabo, String geometry and the noncommutative torus, Commun. Math. Phys. 206 (1999) 603, hep-th/9806099.
10. J. Madore, An introduction to noncommutative differential geometry and its physical applications, London Mathematical Society Lecture Note Series ; 0257, 1999. Another good introduction to NCG with emphasis on fuzzy spaces and Kaluza-Klein.
11. C.P. Martin, J.M. Gracia-Bondia and J.C. Varilly, The standard model as a noncommutative geometry: The low-energy regime, Phys. Rep. 294 (1998) 363, hep-th/9605001. A review of the noncommutative geometry approaches to the standard model.
12. V. Schomerus, D-branes and deformation quantization, JHEP 9906 (1999) 030, hep-th/9903205.
13. T. Schucker, Geometries and forces, in the Proceedings of the European Mathematical Society Summer School on Noncommutative Geometry and Applications, Monsaraz and Lisbon, Paulo Almeida, hep-th/9712095. A review of the Connes approach to Noncommutative Geometry, the standard model and gravity.
14. A. Konechny and A. Schwarz, Introduction to M(atrix) theory and noncommutative geometry, hep-th/0012145; Introduction to M(atrix) theory and noncommutative geometry, Part II, hep-th/0107251. A recent and extensive review.
15. N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 9909 (1999) 032, hep-th/9908142. The main original reference to the connections between strings and noncommutative geometry, noncommutative field theory etc. Largely responsible for the great explosion of interest in this field.
16. D. Sternheimer, Deformation quantization: Twenty years after, proceedings of International Conference on Particles, Fields and Gravitation, Poland, 1998. math.qa/9809056. A relatively recent review on Moyal products, deformation quantization etc.